Yang-mills equations in 4-dimensional conformally connected manifolds

In this paper on the simplest examples of compact 4-dimensional conformally connected manifolds (real quadrics in a 5-dimensional projective space) we show that the only invariant, which is quadratic with respect to the curvature Φ of the connectivity, is the Yang-Mills functional ε |tr (*Φ Λ Φ)|. We do not know whether the 4-form |tr (*Φ Λ Φ)| is invariant in any 4-dimensional conformally connected manifolds.